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Path through a 3x3x3 grid
Posted:
Feb 20, 2013 10:40 AM


There is a (well known) continuous path, made of four straight sections, which passes exactly once through each of 9 points arranged in a square 3x3 array.
Using three of these paths, plus two planetoplane straight sections, it is clearly possible to make a continuous path, made of 14 straight sections, which passes exactly once through each of 27 points arranged in a 3x3x3 grid.
However, there is at least one such path made up of only straight 13 sections.
Can you find such a path?
Suggested notation:
The grid consists of all points (x,y,z) with x, y and z being integers satisfying 0 <= x, y, z <= 2. For a path, give the starting point and all subsequent "target points".
So a path might begin: (0, 0, 2) (2, 2, 0) ...
 Clive Tooth



